Cannot solve uneven beveling due to vertices (?)
Assuming you want to bevel at a 45° angle:
First (with the Ctrl + B hotkey) you need to press C to enable clamp overlay which will make the bevel stop when a bound has been reached.

Then you want to select the mesh and merge by distance (F3 and search it) because the 2 edges will be slid up against each other so that the vertices are very close.
Afterwards you can select the 2 edges forming the bevel and have as many segments as needed.

If you want to make the bevel even bigger, then you can repeat this process again (minus making all the segments) by bevelling the 2 outer edges with 1 segment and with Clamp Overlay turned on. Every time the outer edge meets with another edge, use merge by distance to prevent 2 edges in one place.
You should also join vertices to make sure you don't have an Ngon like so

You can do it like this but the cleaner and more efficient option is just to use less edge loops like what CtrlAltF2 mentioned earlier.
Edit: Additional picture showing the maximum bevels I could do, not pretty though.